iMod: multipurpose normal mode analysis in internal coordinates

Organization of ATP-gated P2X1 receptor intracellular termini in apo and desensitized states

The human P2X1 receptor (hP2X1R) is a trimeric ligand-gated ion channel opened by extracellular ATP. The intracellular amino and carboxyl termini play significant roles in determining the time-course and regulation of channel gating-for example, the C terminus regulates recovery from the desensitized state following agonist washout. This suggests that the intracellular regions of the channel have distinct structural features. Studies on the hP2X3R have shown that the intracellular regions associate to form a cytoplasmic cap in the open state of the channel. However, intracellular features could not be resolved in the agonist-free apo and ATP-bound desensitized structures. Here we investigate the organization of the intracellular regions of hP2X1R in the apo and ATP-bound desensitized states following expression in HEK293 cells. We couple cysteine scanning mutagenesis of residues R25-G30 and H355-R360 with the use of bi-functional cysteine reactive cross-linking compounds of different lengths (MTS-2-MTS, BMB, and BM(PEG)2), which we use as molecular calipers. If two cysteine residues come into close proximity, we predict they will be cross-linked and result in ∼66% of the receptor subunits running on a Western blot as dimers. In the control construct (C349A) that removed the free cysteine C349, and some cysteine-containing mutants, cross-linker treatment does not result in dimerization. However, we detect efficient dimerization for R25C, G30C, P358C, K359C, and R360C. This selective pattern indicates that there is structural organization to these regions in the apo and desensitized states in a native membrane environment. The existence of such precap (apo) and postcap (desensitized) organization of the intracellular domains would facilitate efficient gating of the channel.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

Exploring molecular mechanism of allosteric inhibitor to relieve drug resistance of multiple mutations in HIV-1 protease by enhanced conformational sampling

Recently, allosteric regulations of HIV-1 protease (PR) are suggested as a promising approach to relieve drug resistance of mutations toward inhibitors targeting the active site of PR. Replica-exchange molecular dynamics (REMD) simulations and normal mode analysis (NMA) are integrated to enhance conformational sampling of PR. Molecular mechanics generalized Born surface area (MM-GBSA) method was applied to calculate binding free energies of three inhibitors APV, DRV, and NIT to the wild-type (WT) and multidrug resistance (MDR) PRs. The results suggest that binding free energies of APV and DRV are decreased in the MDR PR relative to the WT PR, suggesting drug resistance of mutations on these two inhibitors. However, the binding ability of the allosteric inhibitor NIT is not impaired in the MDR PR. In addition, internal dynamics analysis based on REMD simulations proves that mutations hardly produce obvious effect on the conformation of the MDR PR in comparison to the WT PR. Scanning of hydrophobic contacts and hydrogen bond contacts of inhibitors with residues of PRs on the concatenated trajectories of REMD demonstrates that mutations change the symmetric interaction networks of APV and DRV with PR, but do not generate obvious influence on the asymmetric interaction network of NIT with PR. In summary, allosteric inhibitor NIT can adapt the MDR PR better than those inhibitors toward the active site of PR, thus allosteric inhibitors of PR may be a possible channel to overcome drug resistance of PR.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

Coarse-grained dynamics of supramolecules: Conformational changes in outer shells of Dengue viruses

While structural data on viruses are more and more common, information on their dynamics is much harder to obtain as those viruses form very large molecular complexes. In this paper, we propose a new method for computing the coarse-grained normal modes of such supra-molecules, NormalGo. A new formalism is developed to represent the Hessian of a quadratic potential using tensor products. This formalism is applied to the Tirion elastic potential, as well as to a Gō like potential. When combined with a fast method for computing a select set of eigenpairs of the Hessian, this new formalism enables the computation of thousands of normal modes of a full viral shell with more than one hundred thousand atoms in less than 2 h on a standard desktop computer. We then compare the two coarse-grained potentials. We show that, despite significant differences in their formulations, the Tirion and the Gō like potentials capture very similar dynamics characteristics of the molecule under study. However, we find that the Gō like potential should be preferred as it leads to less local deformations in the structure of the molecule during normal mode dynamics. Finally, we use NormalGo to characterize the structural transitions that occur when FAB fragments bind to the icosahedral outer shell of serotype 3 of the Dengue virus. We have identified residues at the surface of the outer shell that are important for the transition between the FAB-free and FAB-bound conformations, and therefore potentially useful for the design of antibodies to Dengue viruses.

α-Catenin Structure and Nanoscale Dynamics in Solution and in Complex with F-Actin

As a core component of the adherens junction, α-catenin stabilizes the cadherin/catenin complexes to the actin cytoskeleton for the mechanical coupling of cell-cell adhesion. α-catenin also modulates actin dynamics, cell polarity, and cell-migration functions that are independent of the adherens junction. We have determined the solution structures of the α-catenin monomer and dimer using in-line size-exclusion chromatography small-angle X-ray scattering, as well as the structure of α-catenin dimer in complex to F-actin filament using selective deuteration and contrast-matching small angle neutron scattering. We further present the first observation, to our knowledge, of the nanoscale dynamics of α-catenin by neutron spin-echo spectroscopy, which explicitly reveals the mobile regions of α-catenin that are crucial for binding to F-actin. In solution, the α-catenin monomer is more expanded than either protomer shown in the crystal structure dimer, with the vinculin-binding M fragment and the actin-binding domain being able to adopt different configurations. The α-catenin dimer in solution is also significantly more expanded than the dimer crystal structure, with fewer interdomain and intersubunit contacts than the crystal structure. When in complex to F-actin, the α-catenin dimer has an even more open and extended conformation than in solution, with the actin-binding domain further separated from the main body of the dimer. The α-catenin-assembled F-actin bundle develops into an ordered filament packing arrangement at increasing α-catenin/F-actin molar ratios. Together, the structural and dynamic studies reveal that α-catenin possesses dynamic molecular conformations that prime this protein to function as a mechanosensor protein.

An Alternative Homodimerization Interface of MnmG Reveals a Conformational Dynamics that Is Essential for Its tRNA Modification Function

The Escherichia coli homodimeric proteins MnmE and MnmG form a functional complex, MnmEG, that modifies tRNAs using GTP, methylene-tetrahydrofolate, FAD, and glycine or ammonium. MnmE is a tetrahydrofolate- and GTP-binding protein, whereas MnmG is a FAD-binding protein with each protomer composed of the FAD-binding domain, two insertion domains, and the helical C-terminal domain. The detailed mechanism of the MnmEG-mediated reaction remains unclear partially due to incomplete structural information on the free- and substrate-bound forms of the complex. In this study, we show that MnmG can adopt in solution a dimer arrangement (form I) different from that currently considered as the only biologically active (form II). Normal mode analysis indicates that form I can oscillate in a range of open and closed conformations. Using isothermal titration calorimetry and native red electrophoresis, we show that a form-I open conformation, which can be stabilized in vitro by the formation of an interprotomer disulfide bond between the catalytic C277 residues, appears to be involved in the assembly of the MnmEG catalytic center. We also show that residues R196, D253, R436, R554 and E585 are important for the stabilization of form I and the tRNA modification function. We propose that the form I dynamics regulates the alternative access of MnmE and tRNA to the MnmG FAD active site. Finally, we show that the C-terminal region of MnmG contains a sterile alpha motif domain responsible for tRNA-protein and protein-protein interactions.

Fast, clash-free RNA conformational morphing using molecular junctions

Motivation

Non-coding ribonucleic acids (ncRNA) are functional RNA molecules that are not translated into protein. They are extremely dynamic, adopting diverse conformational substates, which enables them to modulate their interaction with a large number of other molecules. The flexibility of ncRNA provides a challenge for probing their complex 3D conformational landscape, both experimentally and computationally.

Results

Despite their conformational diversity, ncRNAs mostly preserve their secondary structure throughout the dynamic ensemble. Here we present a kinematics-based procedure to morph an RNA molecule between conformational substates, while avoiding inter-atomic clashes. We represent an RNA as a kinematic linkage, with fixed groups of atoms as rigid bodies and rotatable bonds as degrees of freedom. Our procedure maintains RNA secondary structure by treating hydrogen bonds between base pairs as constraints. The constraints define a lower-dimensional, secondary-structure constraint manifold in conformation space, where motions are largely governed by molecular junctions of unpaired nucleotides. On a large benchmark set, we show that our morphing procedure compares favorably to peer algorithms, and can approach goal conformations to within a low all-atom RMSD by directing fewer than 1% of its atoms. Our results suggest that molecular junctions can modulate 3D structural rearrangements, while secondary structure elements guide large parts of the molecule along the transition to the correct final conformation.

Availability and Implementation

The source code, binaries and data are available at https://simtk.org/home/kgs .

Contact

amelie.heliou@polytechnique.edu or vdbedem@stanford.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

The structural basis of flagellin detection by NAIP5: A strategy to limit pathogen immune evasion

Robust innate immune detection of rapidly evolving pathogens is critical for host defense. Nucleotide-binding domain leucine-rich repeat (NLR) proteins function as cytosolic innate immune sensors in plants and animals. However, the structural basis for ligand-induced NLR activation has so far remained unknown. NAIP5 (NLR family, apoptosis inhibitory protein 5) binds the bacterial protein flagellin and assembles with NLRC4 to form a multiprotein complex called an inflammasome. Here we report the cryo-electron microscopy structure of the assembled ~1.4-megadalton flagellin-NAIP5-NLRC4 inflammasome, revealing how a ligand activates an NLR. Six distinct NAIP5 domains contact multiple conserved regions of flagellin, prying NAIP5 into an open and active conformation. We show that innate immune recognition of multiple ligand surfaces is a generalizable strategy that limits pathogen evolution and immune escape.

Flexible Fitting of Atomic Models into Cryo-EM Density Maps Guided by Helix Correspondences

Although electron cryo-microscopy (cryo-EM) has recently achieved resolutions of better than 3 Å, at which point molecular modeling can be done directly from the density map, analysis and annotation of a cryo-EM density map still primarily rely on fitting atomic or homology models to the density map. In this article, we present, to our knowledge, a new method for flexible fitting of known or modeled protein structures into cryo-EM density maps. Unlike existing methods that are guided by local density gradients, our method is guided by correspondences between the α-helices in the density map and model, and does not require an initial rigid-body fitting step. Compared with current methods on both simulated and experimental density maps, our method not only achieves greater accuracy for proteins with large deformations but also runs as fast or faster than many of the other flexible fitting routines.

Structural studies of a hyperthermophilic thymidylate kinase enzyme reveal conformational substates along the reaction coordinate

Thymidylate kinase (TMK) is a key enzyme which plays an important role in DNA synthesis. It belongs to the family of nucleoside monophosphate kinases, several of which undergo structure-encoded conformational changes to perform their function. However, the absence of three-dimensional structures for all the different reaction intermediates of a single TMK homolog hinders a clear understanding of its functional mechanism. We herein report the different conformational states along the reaction coordinate of a hyperthermophilic TMK from Aquifex aeolicus, determined via X-ray diffraction and further validated through normal-mode studies. The analyses implicate an arginine residue in the Lid region in catalysis, which was confirmed through site-directed mutagenesis and subsequent enzyme assays on the wild-type protein and mutants. Furthermore, the enzyme was found to exhibit broad specificity toward phosphate group acceptor nucleotides. Our comprehensive analyses of the conformational landscape of TMK, together with associated biochemical experiments, provide insights into the mechanistic details of TMK-driven catalysis, for example, the order of substrate binding and the reaction mechanism for phosphate transfer. Such a study has utility in the design of potent inhibitors for these enzymes.

DATABASE

Structural data are available in the PDB under the accession numbers 2PBR, 4S2E, 5H5B, 5XAI, 4S35, 5XB2, 5H56, 5XB3, 5H5K, 5XB5, and 5XBH.

NOLB: Nonlinear Rigid Block Normal-Mode Analysis Method

We present a new conceptually simple and computationally efficient method for nonlinear normal-mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues [ Durand et al. Biopolymers 1994 , 34 , 759 - 771 . Tama et al. Proteins: Struct., Funct., Bioinf . 2000 , 41 , 1 - 7 ]. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a nonlinear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy, and topology analyses and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal-mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes/ . A graphical user interface created for the SAMSON software platform will be made available at https://www.samson-connect.net .

Exploring Flexibility of Progesterone Receptor Ligand Binding Domain Using Molecular Dynamics

Progesterone receptor (PR), a member of nuclear receptor (NR) superfamily, plays a vital role for female reproductive tissue development, differentiation and maintenance. PR ligand, such as progesterone, induces conformation changes in PR ligand binding domain (LBD), thus mediates subsequent gene regulation cascades. PR LBD may adopt different conformations upon an agonist or an antagonist binding. These different conformations would trigger distinct transcription events. Therefore, the dynamics of PR LBD would be of general interest to biologists for a deep understanding of its structure-function relationship. However, no apo-form (non-ligand bound) of PR LBD model has been proposed either by experiments or computational methods so far. In this study, we explored the structural dynamics of PR LBD using molecular dynamics simulations and advanced sampling tools in both ligand-bound and the apo-forms. Resolved by the simulation study, helix 11, helix 12 and loop 895–908 (the loop between these two helices) are quite flexible in antagonistic conformation. Several residues, such as Arg899 and Glu723, could form salt-bridging interaction between helix 11 and helix 3, and are important for the PR LBD dynamics. And we also propose that helix 12 in apo-form PR LBD, not like other NR LBDs, such as human estrogen receptor α (ERα) LBD, may not adopt a totally extended conformation. With the aid of umbrella sampling and metadynamics simulations, several stable conformations of apo-form PR LBD have been sampled, which may work as critical structural models for further large scale virtual screening study to discover novel PR ligands for therapeutic application.

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.

Exploring the relationship between vibrational mode locality and coupling using constrained optimization

The use of alternate coordinate systems as a means to improve the efficiency and accuracy of anharmonic vibrational structure analysis has seen renewed interest in recent years. While normal modes (which diagonalize the mass-weighted Hessian matrix) are a typical choice, the delocalized nature of this basis makes it less optimal when anharmonicity is in play. When a set of modes is not designed to treat anharmonicity, anharmonic effects will contribute to inter-mode coupling in an uncontrolled fashion. These effects can be mitigated by introducing locality, but this comes at its own cost of potentially large second-order coupling terms. Herein, a method is described which partially localizes vibrations to connect the fully delocalized and fully localized limits. This allows a balance between the treatment of harmonic and anharmonic coupling, which minimizes the error that arises from neglected coupling terms. Partially localized modes are investigated for a range of model systems including a tetramer of hydrogen fluoride, water dimer, ethene, diphenylethane, and stilbene. Generally, partial localization reaches ∼75% of maximal locality while introducing less than ∼30% of the harmonic coupling of the fully localized system. Furthermore, partial localization produces mode pairs that are spatially separated and thus weakly coupled to one another. It is likely that this property can be exploited in the creation of model Hamiltonians that omit the coupling parameters of the distant (and therefore uncoupled) pairs.

Sensing and signaling of oxidative stress in chloroplasts by inactivation of the SAL1 phosphoadenosine phosphatase

Intracellular signaling during oxidative stress is complex, with organelle-to-nucleus retrograde communication pathways ill-defined or incomplete. Here we identify the 3'-phosphoadenosine 5'-phosphate (PAP) phosphatase SAL1 as a previously unidentified and conserved oxidative stress sensor in plant chloroplasts. Arabidopsis thaliana SAL1 (AtSAL1) senses changes in photosynthetic redox poise, hydrogen peroxide, and superoxide concentrations in chloroplasts via redox regulatory mechanisms. AtSAL1 phosphatase activity is suppressed by dimerization, intramolecular disulfide formation, and glutathionylation, allowing accumulation of its substrate, PAP, a chloroplast stress retrograde signal that regulates expression of plastid redox associated nuclear genes (PRANGs). This redox regulation of SAL1 for activation of chloroplast signaling is conserved in the plant kingdom, and the plant protein has evolved enhanced redox sensitivity compared with its yeast ortholog. Our results indicate that in addition to sulfur metabolism, SAL1 orthologs have evolved secondary functions in oxidative stress sensing in the plant kingdom.

Toward High-Throughput Predictive Modeling of Protein Binding/Unbinding Kinetics

One of the unaddressed challenges in drug discovery is that drug potency determined in vitro is not a reliable indicator of drug activity in vivo. Accumulated evidence suggests that in vivo activity is more strongly correlated with the binding/unbinding kinetics than the equilibrium thermodynamics of protein-ligand interactions (PLIs). However, existing experimental and computational techniques are insufficient in studying the molecular details of kinetics processes of PLIs on a large scale. Consequently, we not only have limited mechanistic understanding of the kinetic processes but also lack a practical platform for high-throughput screening and optimization of drug leads on the basis of their kinetic properties. For the first time, we address this unmet need by integrating coarse-grained normal mode analysis with multitarget machine learning (MTML). To test our method, HIV-1 protease is used as a model system. We find that computational models based on the residue normal mode directionality displacement of PLIs can not only recapitulate the results from all-atom molecular dynamics simulations but also predict protein-ligand binding/unbinding kinetics accurately. When this is combined with energetic features, the accuracy of combined kon and koff prediction reaches 74.35%. Furthermore, our integrated model provides us with new insights into the molecular determinants of the kinetics of PLIs. We propose that the coherent coupling of conformational dynamics and thermodynamic interactions between the receptor and the ligand may play a critical role in determining the kinetic rate constants of PLIs. In conclusion, we demonstrate that residue normal mode directionality displacement can serve as a kinetic fingerprint to capture long-time-scale conformational dynamics of the binding/unbinding kinetics. When this is coupled with MTML, it is possible to screen and optimize compounds on the basis of their binding/unbinding kinetics in a high-throughput fashion. The further development of such computational tools will bridge one of the critical missing links between in vitro compound screening and in vivo drug activity.

EMMPRIN/CD147 is a novel coreceptor of VEGFR-2 mediating its activation by VEGF

EMMPRIN/CD147 is mainly known for its protease inducing function but a role in promoting tumor angiogenesis has also been demonstrated. This study provides evidence that EMMPRIN is a new coreceptor for the VEGFR-2 tyrosine kinase receptor in both endothelial and tumor cells, as it directly interacts with it and regulates its activation by its VEGF ligand, signalling and functional consequences both in vitro and in vivo. Computational docking analyses and mutagenesis studies identified a molecular binding site in the extracellular domain of EMMPRIN located close to the cell membrane and containing the amino acids 195/199. EMMPRIN is overexpressed in cancer and hence is able to further potentiate VEGFR-2 activation, suggesting that a combinatory therapy of an antiangiogenic drug together with an inhibitor of EMMPRIN/VEGFR-2 interaction may have a greater impact on inhibiting angiogenesis and malignancy.

Probing RNA Native Conformational Ensembles with Structural Constraints

Noncoding ribonucleic acids (RNA) play a critical role in a wide variety of cellular processes, ranging from regulating gene expression to post-translational modification and protein synthesis. Their activity is modulated by highly dynamic exchanges between three-dimensional conformational substates, which are difficult to characterize experimentally and computationally. Here, we present an innovative, entirely kinematic computational procedure to efficiently explore the native ensemble of RNA molecules. Our procedure projects degrees of freedom onto a subspace of conformation space defined by distance constraints in the tertiary structure. The dimensionality reduction enables efficient exploration of conformational space. We show that the conformational distributions obtained with our method broadly sample the conformational landscape observed in NMR experiments. Compared to normal mode analysis-based exploration, our procedure diffuses faster through the experimental ensemble while also accessing conformational substates to greater precision. Our results suggest that conformational sampling with a highly reduced but fully atomistic representation of noncoding RNA expresses key features of their dynamic nature.

Enhanced conformational sampling technique provides an energy landscape view of large-scale protein conformational transitions

A novel in silico approach (NMA–ITS) is introduced to rapidly and effectively sample the configuration space and give quantitative data for exploring the conformational changes of proteins.

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

iGNM 2.0: the Gaussian network model database for biomolecular structural dynamics

Gaussian network model (GNM) is a simple yet powerful model for investigating the dynamics of proteins and their complexes. GNM analysis became a broadly used method for assessing the conformational dynamics of biomolecular structures with the development of a user-friendly interface and database, iGNM, in 2005. We present here an updated version, iGNM 2.0 http://gnmdb.csb.pitt.edu/, which covers more than 95% of the structures currently available in the Protein Data Bank (PDB). Advanced search and visualization capabilities, both 2D and 3D, permit users to retrieve information on inter-residue and inter-domain cross-correlations, cooperative modes of motion, the location of hinge sites and energy localization spots. The ability of iGNM 2.0 to provide structural dynamics data on the large majority of PDB structures and, in particular, on their biological assemblies makes it a useful resource for establishing the bridge between structure, dynamics and function.

Understanding nucleotide-regulated FtsZ filament dynamics and the monomer assembly switch with large-scale atomistic simulations

Bacterial cytoskeletal protein FtsZ assembles in a head-to-tail manner, forming dynamic filaments that are essential for cell division. Here, we study their dynamics using unbiased atomistic molecular simulations from representative filament crystal structures. In agreement with experimental data, we find different filament curvatures that are supported by a nucleotide-regulated hinge motion between consecutive FtsZ monomers. Whereas GTP-FtsZ filaments bend and twist in a preferred orientation, thereby burying the nucleotide, the differently curved GDP-FtsZ filaments exhibit a heterogeneous distribution of open and closed interfaces between monomers. We identify a coordinated Mg(2+) ion as the key structural element in closing the nucleotide site and stabilizing GTP filaments, whereas the loss of the contacts with loop T7 from the next monomer in GDP filaments leads to open interfaces that are more prone to depolymerization. We monitored the FtsZ monomer assembly switch, which involves opening/closing of the cleft between the C-terminal domain and the H7 helix, and observed the relaxation of isolated and filament minus-end monomers into the closed-cleft inactive conformation. This result validates the proposed switch between the low-affinity monomeric closed-cleft conformation and the active open-cleft FtsZ conformation within filaments. Finally, we observed how the antibiotic PC190723 suppresses the disassembly switch and allosterically induces closure of the intermonomer interfaces, thus stabilizing the filament. Our studies provide detailed structural and dynamic insights into modulation of both the intrinsic curvature of the FtsZ filaments and the molecular switch coupled to the high-affinity end-wise association of FtsZ monomers.

Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs

Proteins perform their function or interact with partners by exchanging between conformational substates on a wide range of spatiotemporal scales. Structurally characterizing these exchanges is challenging, both experimentally and computationally. Large, diffusional motions are often on timescales that are difficult to access with molecular dynamics simulations, especially for large proteins and their complexes. The low frequency modes of normal mode analysis (NMA) report on molecular fluctuations associated with biological activity. However, NMA is limited to a second order expansion about a minimum of the potential energy function, which limits opportunities to observe diffusional motions. By contrast, kino-geometric conformational sampling (KGS) permits large perturbations while maintaining the exact geometry of explicit conformational constraints, such as hydrogen bonds. Here, we extend KGS and show that a conformational ensemble of the α subunit Gαs of heterotrimeric stimulatory protein Gs exhibits structural features implicated in its activation pathway. Activation of protein Gs by G protein-coupled receptors (GPCRs) is associated with GDP release and large conformational changes of its α-helical domain. Our method reveals a coupled α-helical domain opening motion while, simultaneously, Gαs helix α5 samples an activated conformation. These motions are moderated in the activated state. The motion centers on a dynamic hub near the nucleotide-binding site of Gαs, and radiates to helix α4. We find that comparative NMA-based ensembles underestimate the amplitudes of the motion. Additionally, the ensembles fall short in predicting the accepted direction of the full activation pathway. Taken together, our findings suggest that nullspace sampling with explicit, holonomic constraints yields ensembles that illuminate molecular mechanisms involved in GDP release and protein Gs activation, and further establish conformational coupling between key structural elements of Gαs.

The importance of dynamics in integrative modeling of supramolecular assemblies

Revealing the atomistic architecture of supramolecular complexes is a fundamental step toward a deeper understanding of cellular functioning. To date, this formidable task is facilitated by an emerging array of integrative modeling approaches that combine experimental data from different sources. One major challenge these methods have to face is the treatment of the dynamic rearrangements of the individual subunits upon assembly. While this flexibility can be sampled at different levels, integrating native dynamic determinants with available experimental inputs can provide an effective way to reveal the molecular recognition mechanisms at the basis of supramolecular assembly.

A highly conserved region essential for NMD in the Upf2 N-terminal domain

Upf1, Upf2, and Upf3 are the principal regulators of nonsense-mediated mRNA decay (NMD), a cytoplasmic surveillance pathway that accelerates the degradation of mRNAs undergoing premature translation termination. These three proteins interact with each other, the ribosome, the translation termination machinery, and multiple mRNA decay factors, but the precise mechanism allowing the selective detection and degradation of nonsense-containing transcripts remains elusive. Here, we have determined the crystal structure of the N-terminal mIF4G domain from Saccharomyces cerevisiae Upf2 and identified a highly conserved region in this domain that is essential for NMD and independent of Upf2's binding sites for Upf1 and Upf3. Mutations within this conserved region not only inactivate NMD but also disrupt Upf2 binding to specific proteins, including Dbp6, a DEAD-box helicase. Although current models indicate that Upf2 functions principally as an activator of Upf1 and a bridge between Upf1 and Upf3, our data suggest that it may also serve as a platform for the association of additional factors that play roles in premature translation termination and NMD.

Mapping central α-helix linker mediated conformational transition pathway of calmodulin via simple computational approach

The effects of intrinsic structural flexibility of calmodulin protein on the mechanism of its allosteric conformational transition are investigated in this article. Using a novel in silico approach, the conformational transition pathways of intact calmodulin as well as the isolated N- and C- terminal domains are identified and energetically characterized. It is observed that the central α-helix linker amplifies the structural flexibility of intact Ca(2+)-free calmodulin, which might facilitate the transition of the two domains. As a result, the global conformational transition of Ca(2+)-free calmodulin is initiated by the barrierless transition of two domains and proceeds through the barrier associated unwinding and bending of the central α-helix linker. The binding of Ca(2+) cations to calmodulin further increases the structural flexibility of the C-terminal domain and results in a downhill transition pathway of which all regions transit in a concerted manner. On the other hand, the separation of the N- and C-terminal domains from calmodulin protein loses the mediating function of central α-helix linker, leading to more difficult conformational transitions of both domains. The present study provides novel insights into the correlation of the integrity of protein, the structural flexibility, and the mechanism of conformational transition of proteinlike calmodulin.

Correlated motions are a fundamental property of β-sheets

Correlated motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. The mechanisms that underlie these processes remain largely unknown due mainly to limitations in their direct detection. Here, based on a detailed analysis of protein structures deposited in the protein data bank, as well as on state-of-the art molecular simulations, we provide general evidence for the transfer of structural information by correlated backbone motions, mediated by hydrogen bonds, across β-sheets. We also show that the observed local and long-range correlated motions are mediated by the collective motions of β-sheets and investigate their role in large-scale conformational changes. Correlated motions represent a fundamental property of β-sheets that contributes to protein function.

iMODS: internal coordinates normal mode analysis server

Normal mode analysis (NMA) in internal (dihedral) coordinates naturally reproduces the collective functional motions of biological macromolecules. iMODS facilitates the exploration of such modes and generates feasible transition pathways between two homologous structures, even with large macromolecules. The distinctive internal coordinate formulation improves the efficiency of NMA and extends its applicability while implicitly maintaining stereochemistry. Vibrational analysis, motion animations and morphing trajectories can be easily carried out at different resolution scales almost interactively. The server is versatile; non-specialists can rapidly characterize potential conformational changes, whereas advanced users can customize the model resolution with multiple coarse-grained atomic representations and elastic network potentials. iMODS supports advanced visualization capabilities for illustrating collective motions, including an improved affine-model-based arrow representation of domain dynamics. The generated all-heavy-atoms conformations can be used to introduce flexibility for more advanced modeling or sampling strategies. The server is free and open to all users with no login requirement at http://imods.chaconlab.org.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

A coarse-grained elastic network atom contact model and its use in the simulation of protein dynamics and the prediction of the effect of mutations

Normal mode analysis (NMA) methods are widely used to study dynamic aspects of protein structures. Two critical components of NMA methods are coarse-graining in the level of simplification used to represent protein structures and the choice of potential energy functional form. There is a trade-off between speed and accuracy in different choices. In one extreme one finds accurate but slow molecular-dynamics based methods with all-atom representations and detailed atom potentials. On the other extreme, fast elastic network model (ENM) methods with Cα-only representations and simplified potentials that based on geometry alone, thus oblivious to protein sequence. Here we present ENCoM, an Elastic Network Contact Model that employs a potential energy function that includes a pairwise atom-type non-bonded interaction term and thus makes it possible to consider the effect of the specific nature of amino-acids on dynamics within the context of NMA. ENCoM is as fast as existing ENM methods and outperforms such methods in the generation of conformational ensembles. Here we introduce a new application for NMA methods with the use of ENCoM in the prediction of the effect of mutations on protein stability. While existing methods are based on machine learning or enthalpic considerations, the use of ENCoM, based on vibrational normal modes, is based on entropic considerations. This represents a novel area of application for NMA methods and a novel approach for the prediction of the effect of mutations. We compare ENCoM to a large number of methods in terms of accuracy and self-consistency. We show that the accuracy of ENCoM is comparable to that of the best existing methods. We show that existing methods are biased towards the prediction of destabilizing mutations and that ENCoM is less biased at predicting stabilizing mutations.

Exploring transition pathway and free-energy profile of large-scale protein conformational change by combining normal mode analysis and umbrella sampling molecular dynamics

Large-scale conformational changes of proteins are usually associated with the binding of ligands. Because the conformational changes are often related to the biological functions of proteins, understanding the molecular mechanisms of these motions and the effects of ligand binding becomes very necessary. In the present study, we use the combination of normal-mode analysis and umbrella sampling molecular dynamics simulation to delineate the atomically detailed conformational transition pathways and the associated free-energy landscapes for three well-known protein systems, viz., adenylate kinase (AdK), calmodulin (CaM), and p38α kinase in the absence and presence of respective ligands. For each protein under study, the transient conformations along the conformational transition pathway and thermodynamic observables are in agreement with experimentally and computationally determined ones. The calculated free-energy profiles reveal that AdK and CaM are intrinsically flexible in structures without obvious energy barrier, and their ligand binding shifts the equilibrium from the ligand-free to ligand-bound conformation (population shift mechanism). In contrast, the ligand binding to p38α leads to a large change in free-energy barrier (ΔΔG ≈ 7 kcal/mol), promoting the transition from DFG-in to DFG-out conformation (induced fit mechanism). Moreover, the effect of the protonation of D168 on the conformational change of p38α is also studied, which reduces the free-energy difference between the two functional states of p38α and thus further facilitates the conformational interconversion. Therefore, the present study suggests that the detailed mechanism of ligand binding and the associated conformational transition is not uniform for all kinds of proteins but correlated to their respective biological functions.

Combined approaches to flexible fitting and assessment in virus capsids undergoing conformational change

Fitting of atomic components into electron cryo-microscopy (cryoEM) density maps is routinely used to understand the structure and function of macromolecular machines. Many fitting methods have been developed, but a standard protocol for successful fitting and assessment of fitted models has yet to be agreed upon among the experts in the field. Here, we created and tested a protocol that highlights important issues related to homology modelling, density map segmentation, rigid and flexible fitting, as well as the assessment of fits. As part of it, we use two different flexible fitting methods (Flex-EM and iMODfit) and demonstrate how combining the analysis of multiple fits and model assessment could result in an improved model. The protocol is applied to the case of the mature and empty capsids of Coxsackievirus A7 (CAV7) by flexibly fitting homology models into the corresponding cryoEM density maps at 8.2 and 6.1 Å resolution. As a result, and due to the improved homology models (derived from recently solved crystal structures of a close homolog – EV71 capsid – in mature and empty forms), the final models present an improvement over previously published models. In close agreement with the capsid expansion observed in the EV71 structures, the new CAV7 models reveal that the expansion is accompanied by ∼5° counterclockwise rotation of the asymmetric unit, predominantly contributed by the capsid protein VP1. The protocol could be applied not only to viral capsids but also to many other complexes characterised by a combination of atomic structure modelling and cryoEM density fitting.

iMODFIT: efficient and robust flexible fitting based on vibrational analysis in internal coordinates

Here, we employed the collective motions extracted from Normal Mode Analysis (NMA) in internal coordinates (torsional space) for the flexible fitting of atomic-resolution structures into electron microscopy (EM) density maps. The proposed methodology was validated using a benchmark of simulated cases, highlighting its robustness over the full range of EM resolutions and even over coarse-grained representations. A systematic comparison with other methods further showcased the advantages of this proposed methodology, especially at medium to lower resolutions. Using this method, computational costs and potential overfitting problems are naturally reduced by constraining the search in low-frequency NMA space, where covalent geometry is implicitly maintained. This method also effectively captures the macromolecular changes of a representative set of experimental test cases. We believe that this novel approach will extend the currently available EM hybrid methods to the atomic-level interpretation of large conformational changes and their functional implications.

Conformational transitions in human translin enable nucleic acid binding

Translin is a highly conserved RNA- and DNA-binding protein that plays essential roles in eukaryotic cells. Human translin functions as an octamer, but in the octameric crystallographic structure, the residues responsible for nucleic acid binding are not accessible. Moreover, electron microscopy data reveal very different octameric configurations. Consequently, the functional assembly and the mechanism of nucleic acid binding by the protein remain unclear. Here, we present an integrative study combining small-angle X-ray scattering (SAXS), site-directed mutagenesis, biochemical analysis and computational techniques to address these questions. Our data indicate a significant conformational heterogeneity for translin in solution, formed by a lesser-populated compact octameric state resembling the previously solved X-ray structure, and a highly populated open octameric state that had not been previously identified. On the other hand, our SAXS data and computational analyses of translin in complex with the RNA oligonucleotide (GU)₁₂ show that the internal cavity found in the octameric assemblies can accommodate different nucleic acid conformations. According to this model, the nucleic acid binding residues become accessible for binding, which facilitates the entrance of the nucleic acids into the cavity. Our data thus provide a structural basis for the functions that translin performs in RNA metabolism and transport.

Exploration of conformational transition pathways from coarse-grained simulations

MOTIVATION

A new algorithm to trace conformational transitions in proteins is presented. The method uses discrete molecular dynamics as engine to sample protein conformational space. A multiple minima Go-like potential energy function is used in combination with several enhancing sampling strategies, such as metadynamics, Maxwell Demon molecular dynamics and essential dynamics. The method, which shows an unprecedented computational efficiency, is able to trace a wide range of known experimental transitions. Contrary to simpler methods our strategy does not introduce distortions in the chemical structure of the protein and is able to reproduce well complex non-linear conformational transitions. The method, called GOdMD, can easily introduce additional restraints to the transition (presence of ligand, known intermediate, known maintained contacts, …) and is freely distributed to the community through the Spanish National Bioinformatics Institute (http://mmb.irbbarcelona.org/GOdMD).

AVAILABILITY

Freely available on the web at http://mmb.irbbarcelona.org/GOdMD.

Characterizing conformation changes in proteins through the torsional elastic response

The relationship between functional conformation changes and thermal dynamics of proteins is investigated with the help of the torsional network model (TNM), an elastic network model in torsion angle space that we recently introduced. We propose and test a null-model of "random" conformation changes that assumes that the contributions of normal modes to conformation changes are proportional to their contributions to thermal fluctuations. Deviations from this null model are generally small. When they are large and significant, they consist in conformation changes that are represented by very few low frequency normal modes and overcome small energy barriers. We interpret these features as the result of natural selection favoring the intrinsic protein dynamics consistent with functional conformation changes. These "selected" conformation changes are more frequently associated to ligand binding, and in particular phosphorylation, than to pairs of conformations with the same ligands. This deep relationship between the thermal dynamics of a protein, represented by its normal modes, and its functional dynamics can reconcile in a unique framework the two models of conformation changes, conformational selection and induced fit. The program TNM that computes torsional normal modes and analyzes conformation changes is available upon request. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Structural and functional analysis of coxsackievirus A9 integrin αvβ6 binding and uncoating

Coxsackievirus A9 (CVA9) is an important pathogen of the Picornaviridae family. It utilizes cellular receptors from the integrin αv family for binding to its host cells prior to entry and genome release. Among the integrins tested, it has the highest affinity for αvβ6, which recognizes the arginine-glycine-aspartic acid (RGD) loop present on the C terminus of viral capsid protein, VP1. As the atomic model of CVA9 lacks the RGD loop, we used surface plasmon resonance, electron cryo-microscopy, and image reconstruction to characterize the capsid-integrin interactions and the conformational changes on genome release. We show that the integrin binds to the capsid with nanomolar affinity and that the binding of integrin to the virion does not induce uncoating, thereby implying that further steps are required for release of the genome. Electron cryo-tomography and single-particle image reconstruction revealed variation in the number and conformation of the integrins bound to the capsid, with the integrin footprint mapping close to the predicted site for the exposed RGD loop on VP1. Comparison of empty and RNA-filled capsid reconstructions showed that the capsid undergoes conformational changes when the genome is released, so that the RNA-capsid interactions in the N termini of VP1 and VP4 are lost, VP4 is removed, and the capsid becomes more porous, as has been reported for poliovirus 1, human rhinovirus 2, enterovirus 71, and coxsackievirus A7. These results are important for understanding the structural basis of integrin binding to CVA9 and the molecular events leading to CVA9 cell entry and uncoating.

Design principles of a universal protein degradation machine

The 26S proteasome is a 2.5-MDa, 32-subunit ATP-dependent protease that is responsible for the degradation of ubiquitinated protein targets in all eukaryotic cells. This proteolytic machine consists of a barrel-shaped peptidase capped by a large regulatory particle, which contains a heterohexameric AAA+ unfoldase as well as several structural modules of previously unknown function. Recent electron microscopy (EM) studies have allowed major breakthroughs in understanding the architecture of the regulatory particle, revealing that the additional modules provide a structural framework to position critical, ubiquitin-interacting subunits and thus allow the 26S proteasome to function as a universal degradation machine for a wide variety of protein substrates. The EM studies have also uncovered surprising asymmetries in the spatial arrangement of proteasome subunits, yet the functional significance of these architectural features remains unclear. This review will summarize the recent findings on 26S proteasome structure and discuss the mechanistic implications for substrate binding, deubiquitination, unfolding, and degradation.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Flexible protein docking refinement using pose-dependent normal mode analysis

Modeling conformational changes in protein docking calculations is challenging. To make the calculations tractable, most current docking algorithms typically treat proteins as rigid bodies and use soft scoring functions that implicitly accommodate some degree of flexibility. Alternatively, ensembles of structures generated from molecular dynamics (MD) may be cross-docked. However, such combinatorial approaches can produce many thousands or even millions of docking poses, and require fast and sensitive scoring functions to distinguish them. Here, we present a novel approach called "EigenHex," which is based on normal mode analyses (NMAs) of a simple elastic network model of protein flexibility. We initially assume that the proteins to be docked are rigid, and we begin by performing conventional soft docking using the Hex polar Fourier correlation algorithm. We then apply a pose-dependent NMA to each of the top 1000 rigid body docking solutions, and we sample and re-score multiple perturbed docking conformations generated from linear combinations of up to 20 eigenvectors using a multi-threaded particle swarm optimization algorithm. When applied to the 63 "rigid body" targets of the Protein Docking Benchmark version 2.0, our results show that sampling and re-scoring from just one to three eigenvectors gives a modest but consistent improvement for these targets. Thus, pose-dependent NMA avoids the need to sample multiple eigenvectors and it offers a promising alternative to combinatorial cross-docking.